Optical diagnostics with radiation trapping effect in low density and low temperaturehelium plasmaWonwook Lee, Kyungdeuk Park, Duck-Hee Kwon, and Cha-Hwan Oh Citation: Physics of Plasmas 23, 063516 (2016); doi: 10.1063/1.4954047 View online: http://dx.doi.org/10.1063/1.4954047 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/23/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in One-dimensional time-dependent fluid model of a very high density low-pressure inductively coupled plasma J. Appl. Phys. 118, 243303 (2015); 10.1063/1.4938490 Electrical characterization of the flowing afterglow of N2 and N2/O2 microwave plasmas at reduced pressure J. Appl. Phys. 115, 163303 (2014); 10.1063/1.4872468 Comparison between experiment and simulation for argon inductively coupled plasma Phys. Plasmas 16, 113502 (2009); 10.1063/1.3261836 Role of low-frequency power in dual-frequency capacitive discharges Appl. Phys. Lett. 95, 111502 (2009); 10.1063/1.3223593 Effect of argon additive on H − density and temperature in volume negative ion source Rev. Sci. Instrum. 75, 1747 (2004); 10.1063/1.1695618

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Optical diagnostics with radiation trapping effect in low density and lowtemperature helium plasma

Wonwook Lee,1,a) Kyungdeuk Park,2 Duck-Hee Kwon,1 and Cha-Hwan Oh21Nuclear Data Center, Korea Atomic Energy Research Institute, Daejeon 34057, South Korea2Department of Physics, Hanyang University, Seoul 04763, South Korea

(Received 19 January 2016; accepted 3 June 2016; published online 16 June 2016)

Low density (ne< 1011 cm�3) and low temperature (Te< 10 eV) helium plasma was generated by

hot filament discharge. Electron temperature and density of neutral helium plasma were measured

by Langmuir probe and were determined by line intensity ratio method using optical emission

spectroscopy with population modelings. Simple corona model and collisional-radiative (CR)

model without consideration for radiation trapping effect are applied. In addition, CR model taking

into account the radiation trapping effect (RTE) is adopted. The change of single line intensity ratio

as a function of electron temperature and density were investigated when the RTE is included and

excluded. The changes of multi line intensity ratios as a function of electron temperature were

scanned for various radiative-excitation rate coefficients from the ground state and the helium gas

pressures related with the RTE. Our CR modeling with RTE results in fairly better agreement of

the spectroscopic diagnostics for the plasma temperature or density with the Langmuir probe meas-

urements for various helium gas pressures than corona modeling and CR modeling without RTE.

Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4954047]

I. INTRODUCTION

Optical emission spectroscopy (OES) is a widely used

plasma diagnostics tool because OES is easy to measure,

does not disturb plasmas during the measurement, and its

measurement system is simple.1 Plasma diagnostics using

OES are based on comparison between theoretical and ex-

perimental transition line intensity ratios. The theoretical

transition line intensities and their ratio can be expected by a

population modeling.2,3 Population densities of excited states

are the functions of plasma parameters, such as electron tem-

perature and density. Therefore, electron temperature (Te)and density (ne) can be determined from the matching of thetheoretically modeled and the experimentally measured line

intensity ratios.

Corona model has been normally adopted for low den-

sity plasma (ne< 1011 cm�3) as a population model. Optical

diagnostics using corona model have been applied to neon

(Ne), argon (Ar), and their mixture plasmas and compared

with another diagnostics method, such as Langmuir probe

(LP). Based on the evaluation with another diagnostic

method, OES synthesized with corona model has been suc-

cessfully applied to determine the electron temperature for

Ne4 and Ar5–7 in electron density (ne< 1011 cm�3) and tem-

perature range (Te< 5 eV).The optical diagnostics with corona model has been

applied to low density helium (He) plasma as well. Boivin

et al.8 calculated the line intensity ratio of 504.8 nm/471.3 nm by corona model against various Te and measuredelectron temperature and density with LP. Electron tempera-

ture by corona model agreed with Te� 10 eV by LP inne< 10

11 cm�3 with reasonable accuracy. However, Podder

et al.9 reported that their calculated line intensity ratios bycorona model show large difference with the measured line

intensity ratio at Te< 5 eV even for similar electron densitywith Boivin’s experiment. They suggested that collisional-

radiative (CR) model with radiation trapping effect (RTE) in

He plasma has to be taken into account in the population

model.

RTE has been called as the induced absorption effect of

atoms, stimulated absorption effect, self-absorption effect of

photon, photo-excitation effect, and so on. The effect has

been usually neglected in optically thin plasma. Since He

CR modeling with radiative-excitation rate coefficient has

been suggested by Sawada et al.,10 various He plasmas havebeen diagnosed by CR model with RTE.10–13 Especially,

Kajita and Ohno13 compared optically diagnosed electron

temperature and density by CR model with RTE with the LP

measurement for high density (ne> 1011 cm�3) He plasma.

However, in low density He plasma, the optically diagnosed

plasma parameters by CR model with RTE have not been

tested with another diagnostic method.

In this paper, we determined electron temperature and

density by using CR model with RTE for low density

(ne< 1011 cm�3) He plasma. The optically diagnosed param-

eters were compared with the measured parameters with LP.

Also, our CR modeling with RTE for line intensity ratios

was extended to plasma density and temperature regions

beyond the low density and the low temperature to verify in

which density and temperature regions in RTE are

significant.

This paper is organized as follows. In Section II, line in-

tensity ratio method for optical diagnostics will be described

in detail. In Section III, experimental apparatus and condi-

tions for hot filament discharge will be stated. In Section IV,

the RTE on the line intensity ratios will be discussed in detaila)Electronic mail: wwlee@kaeri.re.kr

1070-664X/2016/23(6)/063516/6/$30.00 Published by AIP Publishing.23, 063516-1

PHYSICS OF PLASMAS 23, 063516 (2016)

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for CR modeling with RTE. The optically diagnosed electron

temperatures and densities by various population models

will be compared with the LP measurement, temperature by

simple corona model, and temperature and density by CR

modeling without RTE. Finally, our results will be briefly

concluded in Section V.

II. LINE INTENSITY RATIO METHOD

The radiation intensity from plasma Iki is given byIki¼EkiNkAki (W/cm3) where Eki is the energy differencebetween energy states Ei and Ek (Ek>Ei), Aki is the transitionprobability, and Nk is the population density of upper energystate k. The line intensity ratio L can be expressed by

L ¼ IkiIpq¼ kpqNkAki

kkiNpApq; (1)

where kki is the transition wavelength from energy states kto i.

Population densities of state Nk and Np in Eq. (1) can bedetermined by kinetics modelings depending on electron

temperature and density of plasma.2,3

A. Population density models

Simple model for low density plasma is corona model

which assumes that electron impact excitation and de-

excitation between excited atoms and ions are neglected and

spontaneous transition is only allowed by the depopulation

process.1–3,8,9 In this assumption, population density of kstate is governed by the balance between the electron impact

excitation from ground state to the state k and the spontane-ous emission from k state, i.e.,

NgneCgkðTeÞ ¼ NkXi

states as well as the ground state, the population density of

excited states except that of metastable states is given

by10,11,17

Np ¼ r0neNþ þ r1neNg þ r2neNð21SÞ þ r3neNð23SÞ; (6)

where N(21S) and N(23S) are the population densities of met-astable states 21S and 23S, respectively. r0, r1, r2, and r3 arepopulation coefficients in Eq. (6). The first term represents

the recombining plasma component and the other terms cor-

respond to the ionizing plasma components in Eq. (6).3,17,18

In our CR model calculation, the source for excitation/de-ex-

citation rate coefficients, wavelengths, and transition proba-

bilities is same as that in our corona model calculation stated

above. Other atomic data for the rate equation are same as

those used in the CR modeling by Goto.17–24 The population

density obtained in this manner is used to determine the line

intensity ratio of Eq. (1).

B. Radiation trapping effect

When plasma is optically thick, the radiation measured

by detector becomes smaller than the radiation produced in

plasma due to RTE. RTE is based on the induced absorption

process of atoms where radiation spontaneously emitted by an

atom is absorbed by another atoms in plasma. The attenuated

radiation intensity through plasma is a function of the absorp-

tion coefficient kpq ¼ h�pqnpBpqI�=c3,25 where np is the popu-lation density of lower state p in the RTE process, h is thePlanck’s constant, h�pq is the energy difference between pstate and the higher q state, Bpq is the Einstein B-coefficient,I� is the line shape function, and c is the speed of light. Thus,RTE is a function of population density of lower state.

For low density plasma, optical depth is normally thin

and is negligible. Corona model successfully determines the

electron temperature for low density Ne and Ar plasma with-

out considering RTE.4–6 However, for low density He

plasma, RTE from ground state to excited states is not negli-

gible,10,13,26 while RTE between the excited states is negligi-

ble since most of the population is in the ground state. CR

model including dominant RTEs from ground state to

excited states for He is given by

Np ¼ r0neNþ þ r1neNg þ r2neNð21SÞ þ r3neNð23SÞþ r4K31PNg þ r5K41PNg; (7)

where K31P and K41P are radiative-excitation rate coefficientsfrom the ground state to excited states 31P and 41P, respec-

tively.10,13 r4 and r5 are the population coefficients. In ourCR-model calculation, RTEs for 31P and 41P are taken into

account.

III. EXPERIMENTAL SETUP

Low density plasma was generated with hot filament

discharge in a vacuum vessel as shown in Fig. 2(a). The

details of vacuum vessel and hot filament configuration are

described in Ref. 14. The He plasma was produced by the

discharging power of about 150 V/7.8 A and was maintained

through adjusting the heating power for the hot filament. The

base pressure was �3� 10�5 Torr. He gas was injected andthe gas pressure was controlled and maintained by mass-

flow-rate controller (MFC) during the measurement. The

plasma parameters were measured at the pressure of

0.005–0.045 Torr. The gas pressure was adapted so that He

transition lines clearly distinguished and plasma was main-

tained stably. He particle density was calculated from He gas

pressure by ideal gas law at room temperature and we

assumed that He particle density was same to the population

density of ground state.

LP was installed on top of the vacuum vessel to measure

electron temperature and density, and located at the center of

the vacuum vessel as shown in Fig. 2(a). An optical fiber

with a core diameter of 400 lm collected radiation fromplasma and transferred the radiation to a spectrometer. The

optical fiber was placed toward the end of the LP as shown

in Fig. 2(a). The spectrum of radiation was analyzed with a

portable spectrometer (HR4000, Oceanoptics). Wavelength

range of the spectrometer was 200 nm–1100 nm with resolu-

tion of �1 nm. All optical systems of viewport, optical fiber,and spectrometer were relatively calibrated with a quartz

tungsten halogen lamp (63976, ORIEL). Exposure time of

the spectrometer was 50 ms and the spectra of plasma were

averaged for 10 times the measurements. Fig. 2(b) shows the

spectrum of He plasma whose background spectrum without

discharge was measured for every spectrum of He plasma

and eliminated.

FIG. 2. (a) Schematic diagram for hot filament discharge and (b) spectrum

of He plasma by hot filament discharge.

063516-3 Lee et al. Phys. Plasmas 23, 063516 (2016)

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IV. RESULTS AND DISCUSSION

In order to discuss the line intensity ratio variation

depending on RTE, contour plots for line intensity ratio of

504.8 nm (41S – 21P)/471.3 nm (43S – 23P) are displayed as a

function of (Te, ne) for chosen population densities of metasta-ble states and radiative-excitation rate coefficient in Fig. 3.

Line intensity ratio not considering RTE is almost independ-

ent of electron density in ne< 1010 cm�3 while the line inten-

sity ratio changes as a function of not only electron

temperature but also electron density in ne> 1010cm�3, as

shown in Fig. 3(a). When electron temperature decreases the

line intensity ratio in Fig. 3(a) decreases monotonically. Thus,

the line intensity ratio of 504.8 nm/471.3 nm can be used to

determine the electron temperature by corona model depend-

ing only on the electron temperature without RTE in the low

electron density region of ne< 1010 cm�3. When RTE is con-

sidered, the line intensity ratio changes as shown in Fig. 3(b).

In the low electron density region ne< 1010 cm�3, the line in-

tensity ratio for Te< 10 eV changes as functions of not onlythe electron temperature but also the electron density.

However, in the low electron density region the line intensity

ratio for Te> 10 eV is insensitive to the electron density assimilar as in Fig. 3(a). Therefore, the RTE becomes significant

in the low density and low temperature He plasma.

Fig. 4 shows the line intensity ratios for various transitions

as a function of electron temperature when the radiative-

excitation rate coefficient increased from 10�1 to 103 and the

gas pressure is increased from 0.006 Torr to 0.06 Torr where

N(21S)¼ 5� 103cm�3, N(23S)¼ 5� 109cm�3, and ne¼ 5� 109 cm�3. Line intensity ratio as a function of electron tem-perature for the radiative-excitation rate coefficients and the

ground state density according to the gas pressure are different

for various transition lines as shown in Figs. 4(a)–4(d). The

line intensity ratios change largely in Te< 10 eV and have thesame value in Te> 10 eV when radiative-excitation rate coeffi-cient K31P increases to 10

1. As well line intensity ratios change

more sensitively in Te< 5 eV when the gas pressure is high.The line intensity ratio of 501.6 nm (31P – 21S)/728.1 nm is

about 75 and is almost constant in Te< 2 eV when RTE is con-sidered. The population density of 31P state is the most effec-

tive on the RTE and the population density in Te< 2 eV ismainly determined by RTE. As electron temperature increases

and the electron-impact excitation and de-excitation processes

become large in Te> 2 eV, the line intensity ratio of 501.6 nm/728.1 nm changes rapidly and meets the line intensity ratio not

considering RTE. Therefore, RTE is the dominant process in

low temperature (Te< 10 eV) and low density (ne< 1011 cm�3)

He plasma.

In corona model, line intensity ratio is given as a func-

tion of only electron temperature, because Cgk in Eq. (3) is afunction of electron temperature. The electron temperature

of the discharged plasma can be simply determined by com-

paring the measured line intensity ratio with the line inten-

sity ratio calculated by corona model. However, in CR

model, line intensity ratio is given as a function of more

plasma parameters. Electron temperature and electron den-

sity in CR model are determined as the values minimizing

the error function

ferr Te; ne;N 21Sð Þ;N 23Sð Þ;K31P;K41P

� �

¼X Lexp � LCR

LCR

� �2; (8)

where Lexp and LCR are the line intensity ratios determinedby experiment and CR model, respectively.

Fig. 5 shows the diagnosed electron temperatures and

densities against He pressure and these plasma parameters

are measured by LP and determined by OES combined with

population modeling. The gray triangles represent electron

temperature determined by corona model. Single line inten-

sity ratio of 504.8 nm (41S – 21P)/471.3 nm (43S – 23P) is

selected to compare with the previous results.8,9 The blue

diamonds and red circles represent electron temperature and

densities which are determined by CR-model with RTE and

without RTE, respectively. Five intensity ratios of 667.8 nm

FIG. 3. Line intensity ratios of (a) 504.8 nm/471.3 nm without RTE and (b)

with RTE as a function of electron density and electron temperature where

N(21S)¼ 5� 103 cm�3, N(23S)¼ 5� 109cm�3, K41P ¼ 0:1, and Ng¼ 1.93� 1014cm�3.

063516-4 Lee et al. Phys. Plasmas 23, 063516 (2016)

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2016 00:02:35

(31D – 21P)/728.1 nm (31S – 21P), 728.1 nm/706.5 nm (33S –

23P), 501.6 nm (31P – 21S)/728.1 nm, 447.2 nm (43D – 23P)/

706.5 nm, and 492.2 nm (41D – 21P)/728.1 nm are selected in

the determination of the electron temperature and the elec-

tron density by minimizing the error function of Eq. (8). The

set of plasma parameters which minimized the error function

ferr are displayed with the averaged value for ten sets and theerror bars which denote the maximum difference. ferr forCR-model without RTE are minimized at over than 0.96,

while ferr for CR-model with RTE are minimized at less than0.045. The value of ferr> 0.96 means it is impossible for CRmodel without RTE to obtain the value which simultane-

ously satisfies five line intensity ratios. Especially, the meas-

ured intensity of 501.6 nm (31P – 21S) is larger than that of

728.1 nm and the measured line intensity ratios of 501.6 nm/

728.1 nm are 2–2.5 while the determined intensity by the

CR-model without RTE is smaller than that of 728.1 nm and

the ratio is less than 0.1. Thus, the CR-model not considering

RTE cannot exactly expect the measured line intensity ratios

of low density and low temperature He plasma.

As He pressure increases, the electron temperature

decreases and electron density increases in the case of LP

measurement as shown in Figs. 5(a) and 5(b). The electron

temperatures by corona model are much higher than the LP

measurement and show different values for the LP measure-

ment when the gas pressure increases. Also, the electron

temperatures and densities determined by CR-model without

RTE have large different values from the LP measurement

when gas pressure changes. The discrepancy for electron

temperature and density as well as their change against gas

pressure is greatly resolved by CR model with RTE. The

electron temperatures and densities by CR model with RTE

are in good agreement with the LP measurement as shown in

Fig. 5.

V. CONCLUSION

We have calculated the population densities of He I

excited states by corona, CR model with RTE, and CR model

without RTE and performed various parametric studies for the

line intensity ratio by the CR model with RTE. When RTE

was considered, the line intensity ratios have changed in low

electron density (ne< 1011 cm�3) region. Line intensity ratios

are sensitive to RTE in Te< 10 eV and RTE can be negligible

FIG. 4. Line intensity ratios for (a)

504.8 nm/471.3 nm, (b) 492.2 nm/

728.1 nm, (c) 667.8 nm/728.1 nm, and (d)

501.6 nm/728.1 nm as a function of elec-

tron temperature at electron density of

ne¼ 5� 109cm�3 for various radiative-excitation rate coefficients. Black and red

lines represent the line intensity ratios

where He gas pressure are 0.006 Torr

(Ng¼ 1.93� 1014cm�3) and 0.06 Torr(Ng¼ 1.93� 1015cm�3), respectively.Solid lines represent the line intensity

ratios without RTE and dashed, dashed-

dotted, and dotted lines represent the line

intensity ratios by considering RTE with

the coefficients K31P ¼ 10�1, 101, and103, respectively, where N(21S)¼ 5� 103cm�3 and N(23S)¼ 5� 109cm�3.

FIG. 5. (a) Electron temperatures by the LP measurement and by OES com-

bined with corona model and CR model and (b) electron densities by the LP

measurement and by OES combined with CR model as a function of He gas

pressure. Five line intensity ratios (see the text of Sec. IV) were selected to

determine the electron temperature and the density by the OES with the CR

models.

063516-5 Lee et al. Phys. Plasmas 23, 063516 (2016)

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in Te> 10 eV. RTE is the most dominant processes in lowdensity (ne< 10

11 cm�3) and low temperature (Te< 10 eV) Heplasma. In order to determine electron temperature and density

of He plasma, we have generated low density (ne< 1011 cm�3)

and low temperature (Te< 10 eV) He plasma and measuredelectron temperature and density with LP and by OES with

various population modelings for different gas pressures.

When RTE is neglected, the optically diagnosed electron tem-

peratures with the corona and the CR modeling show large dif-

ference with those by the LP measurement. When RTE is

taken into account for CR modeling, the electron density and

temperature are in good agreement with those by the LP

measurement.

ACKNOWLEDGMENTS

The authors wish to express their thanks to Dr. M. Goto

for valuable discussions. This research was supported by

National R & D Program funded by the Korean Ministry of

Science, ICT, and Future Planning.

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